Loan Ranger

A young person turns eighteen and heads off to college or perhaps starts working. He is blasted with offers of easy credit. Low introductory rates, free t-shirts and water bottles, and access to quick cash entice him to sign up. Then, he goes shopping. Without a basic understanding of how credit works, he can get thousands into debt before he even knows what hit him!

Of course, credit is a complicated topic. This lesson focuses on the basics of borrowing with a credit card including interest rates, monthly compounding intervals, and different payback options. By comparing a few different scenarios, students will understand how much an item can really end up costing when it's purchased with a credit card.

Students will

Compare the consequences of not paying balances on two cards with different APRs

Observe the effect of adding monthly compounding to the model

Compare the effect of paying the minimum versus paying more in how much interest is paid

Compare the effect of paying the minimum versus paying more in how long it takes to pay off the balance

Before you begin

Students should be able to calculate a percent increase of r% by multiplying by 1 + r. Familiarity with expressing percent growth as an exponential function is helpful, but not assumed. When calculating successive balances after payments are made, students will use either their calculators or spreadsheets to carry out a recursive process. If they aren't familiar with these techniques, you will need to demonstrate.

What's the ideal size for a soda can? Students use the formulas for surface area and volume of a cylinder to design different cans, calculate their cost of production, and find the can that uses the least material to contain a standard 12 ounces of liquid.

How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.

Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

What’s the best strategy for creating a March Madness bracket? Students use probability to discover that it’s basically impossible to correctly predict every game in the tournament. Nevertheless, that doesn’t stop people from trying.

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

Topic:
Building Functions (BF), Interpreting Functions (IF), Using Probability to Make Decisions (MD)

How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.

How do noise-canceling headphones work? In this lesson, students use transformations of trigonometric functions to explore how sound waves can interfere with one another, and how noise-canceling headphones use incoming sounds to figure out how to produce that sweet, sweet silence.

How much should companies pay their employees? Students graph and solve systems of linear equations in order to examine the effects of wage levels on labor and consumer markets, and they discuss the possible pros and cons of increasing the minimum wage.

Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.

How have video game console speeds changed over time? Students write an exponential function based on the Atari 2600 and Moore's Law, and see whether the model was correct for subsequent video game consoles.

Like the jacket, this lesson is for Members only.

Some Free Lessons From Mathalicious

How do the rules of an election affect who wins? Students calculate (as a percent) how much of the electoral and popular vote different presidential candidates have received, and add with integers to explore elections under possible alternative voting systems.

Topic:
Number System (NS), Ratios and Proportional Relationships (RP), Reasoning with Equations and Inequalities (REI)